The effect of extension on the structure of filaments of 6.6-nylon

Modifications to the structure of filaments of 6.6 nylon, due to extension at various rates, have been investigated by optical and X-ray methods. Stable changes in the density and the principal X-ray spacings have been observed together with a reversible transition, during extension, of the kind noted byBrill.

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Zusammenfassung Strukturänderungen an 6.6-Nylonseide, hervorgerufen durch Verstrecken mit verschiedenen Geschwindigkeiten, werden mittels optischer und röntgenographischer Methoden untersucht. Es werden während der Verstreckung bleibende Veränderungen der Dichte und der Hauptebenenabstände sowie einBrillscher umkehrbarer Übergang beobachtet.

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Résumé Moyennant des méthodes optiques et radiologiques on a etudié des modifications de la structure des fils de nylon 6.6 entraînées á plusieurs vitesses d'allongement. On a observé des changements définitifs de la densité et des distances réticulaires principales ainsi qu'une transition reversible, du type constaté parBrill, au cours de l'allongement.

     

Asymptotic Behaviour of a Pile-Up of Infinite Walls of Edge Dislocations

We consider a system of parallel straight edge dislocations and we analyse its asymptotic behaviour in the limit of many dislocations. The dislocations are represented by points in a plane, and they are arranged in vertical walls; each wall is free to move in the horizontal direction. The system is described by a discrete energy depending on the one-dimensional horizontal positions x _i > 0 of the n walls; the energy contains contributions from repulsive pairwise interactions between all walls, a global shear stress forcing the walls to the left, and a pinned wall at x = 0 that prevents the walls from leaving through the left boundary. We study the behaviour of the energy as the number of walls, n, tends to infinity, and characterise this behaviour in terms of Γ-convergence. There are five different cases, depending on the asymptotic behaviour of the single dimensionless parameter β _n , corresponding to ${\beta_n \ll 1/n, 1/n \ll \beta_n \ll 1}$ , and ${\beta_n \gg 1}$ , and the two critical regimes β _n ~ 1/n and β _n ~ 1. As a consequence we obtain characterisations of the limiting behaviour of stationary states in each of these five regimes. The results shed new light on the open problem of upscaling large numbers of dislocations. We show how various existing upscaled models arise as special cases of the theorems of this paper. The wide variety of behaviour suggests that upscaled models should incorporate more information than just dislocation densities. This additional information is encoded in the limit of the dimensionless parameter β _n .     

Investigation of the stability problems of elastic bodies using the method of mathematical theory of elasticity

In this paper, using the equilibrium equations and boundary conditions of elastic stability problem of and the method of mathematical theory of elasticity, we solve some elastic stability problems, which were studied by Ишлынский^[2] and Войцеховская^[3,4],and obtained more reasonable results than theirs.     

Application of complex path-independent integrals to problems of bending of thin elastic plates

Summary Complex path-independent integrals have been already widely applied to problems of plane and antiplane elasticity for the determination of a variety of quantities of interest including stress intensity factors, loading intensities and the positions of geometrical characteristic lengths of singularities in the elastic field (like cracks, holes and inclusions). In this paper, we show that the same results apply also to the case of problems of thin isotropic elastic plates under bending where the complex-variable formulation is also valid. We make reference to the experimental methods which are appropriate for these integrals in an engineering environment and, finally, we apply this approach to the location of a circular hole in the problem of bending of a thin plate. Numerical results are also presented.

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Die Anwendung komplexer, wegunabhängiger Integrale bei Biegeproblemen dünner elastischer Platten

Übersicht Komplexe, wegunabhängige Integrale wurden schon häufig bei ebenen und antiplanaren Elastizitätsproblemen benutzt, etwa zur Ermittlung von Spannungskonzentrationsfaktoren, Lastintensitäten und der Position charakteristischer geometrischer Größen von Singularitäten im elastischen Feld (wie bei Rissen, Löchern und Einschlüssen). Es wird hier gezeigt, daß diese Ergebnisse auf Biegeprobleme dünner, isotrop-elastischer Platten übertagbar sind, da die Formulierung mit komplexen Variablen ebenfalls gültig ist. Auf die experimentellen Methoden, die für die ingenieurmäßige Ausnutzung geeignet sind, wird hingewiesen und dies wird erläutert anhand der Lokalisierung eines Kreislochs in einer gebogenen dünner Platte; numerische Resultate dazu werden angegeben.

     

Boundaries of the plasma-free regime of electroexplosion of a foil

Results of the experimental studies of the commutation characteristics of an electroexplosive breaker upon heating of a copper foil by a current pulse of duration τ≈1msec are given. The dependences of the electric-field strength and the specific power of the circuit breaker during an electroexplosion of the foil on the specific power of the source P_s are found and it is shown that the transition of the plasma-free regime of electroexplosion of the foil to a plasma regime occurs for P_s=30–40GW/g. Institute of Experimental Physics, Sarov 607190. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 14–20, January–February, 2000.     

Investigation of the Structure of the Set of Continuous Solutions of Systems of Linear Difference Equations with Continuous Argument

We obtain conditions for the existence of continuous and N-periodic solutions, where N is a positive integer number, for systems of linear difference equations with continuous argument and investigate the structure of the set of these solutions. __________ Translated from Neliniini Kolyvannya, Vol. 8, No. 3, pp. 351–359, July–September, 2005.     

Sufficient Conditions for the Existence of Bounded Solutions of Systems of Nonlinear Difference Equations

We obtain sufficient conditions for systems of nonlinear difference equations x(n + 1) = A(x(n))x(n) + f(n), n ∈ ℤ, where A(x) is a matrix function continuous on ℝ ^m , to have solutions in the space of bilateral number sequences. __________ Translated from Neliniini Kolyvannya, Vol. 8, No. 2, pp. 165–173, April–June, 2005.     

Some specific features of high-temperature deformation of materials

Experimental results for high-temperature deformation of an iron-based structural material in the temperature ranges including the points of the Fe_α→Fe_β→Fe_ψ transition are given. It is shown that the strain-strength properties of the material change nonmonotonically on the interval 700°C<T<1000°C and that the internal phase-structural changes exert an effect on the thermal effects. Approximating dependences that permit one to describe deformation processes in the indicated temperature ranges upon uniaxial loading are proposed. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 152–156, November–December, 1999.     

Approximate determinations of the center of shear by use of the St. Venant solution for the flexure problem of plates of variable thickness

Summary We extend a recent analysis of the shear center problem in the context of the linear theory of transverse bending of orthotropic elastic plates by an explicit comparison of results based on several differing definitions of the center of shear within the framework of the St. Venant flexure solution for the problem of orthotropic plates. We also consider transverse bending of anisotropic plates where we find a significant aspect ratio effect not present in the orthotropic, case, and the shear center problem for plates with combined midplane bending and stretching as a consequence of constitutive coupling.

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Näherungsweise Bestimmungen des Schubmittelpunks für Platten variabler Dicke im Rahmen der St. Venant'schen Querkraft-Biegungslösung

Übersicht Eine kürzliche Analyse des Schubmittelpunktproblems als ein Problem der linearen Theorie orthotroper elastischer Platten wird erweitert durch einen Vergleich von Resultaten auf Grund von verschiedenen Definitionen des Schubmittelpunkts im Rahmen des St. Venant'schen Ansatzes für das Querkraft-Biegeproblem. In Ergänzung dieser Betrachtungen wird eine Bestimmung des Schubmittelpunkts anisotroper Platten ausgeführt, welche, im Unterschied zum orthotropen Fall, einen ausgeprägten Einfluß der Plattenlänge zeigt. Weiterhin behandelt wird das Schubmittelpunktproblem für Platten, für welche Biegung und Streckung durch das Stoffgesetz gekoppelt sind.

     

The center of shear as a problem of the theory of plates of variable thickness

Summary The principal concern of this paper is to focus once again attention on the inherent difficulties which are associated with attempts to determine shear center locations for beams of given cross section on the basis of the classical St. Venant torsion-flexure analysis. The special case of this problem which is given when the beam may be treated as a thin plate of variable thickness is used to bring out the limited significance of the St. Venant formulas in relation to the higher-dimension mixed boundary value problem which has previously been shown to be at the root of the shear center problem.

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Der Schubmittelpunkt als ein Problem der Theorie von Platten veränderlicher Dicke

Übersicht Der Beitrag wendet sich nochmals den Schwierigkeiten zu, die bei der Bestimmung der Lage des Sehubmittelpunkts für gegebene Balkenquerschnitte auftreten, wenn man das Problem mit Hilfe der klassischen St. Venant-Biegetheorie behandelt. Der Sonderfall des Problems, bei dem der Balken als dünne Platte veränderlicher Dicke betrachtet wird, dient zur Aufdeckung der Bedeutung der St. Venant-Formeln im Verhältnis zu dem zweidimensionalen Randwertproblem, dessen für das Schubmittelpunktsproblem grundlegende Eigenschaft früher gezeigt worden war.

     

On the structure of the set of continuously differentiable solutions of one boundary-value problem for a system of functional differential equations of neutral type

We study the structure of the set of solutions, continuously differentiable for t ∈ R ⁺ = [0; + ∞), of one limit problem for systems of nonlinear functional differential equations of neutral type with nonlinear deviations of argument that depend on an unknown function. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 277–289, April–June, 2007.     

Asymptotics of the trajectory of an interval that contains the preimage of a periodic point

We consider dynamical systems defined by continuous maps of an interval I of the real axis into itself. We prove that if an interval J in I contains the preimage of a periodic point of period p of a map f ∈ C ⁰(I, I), then the sequence of intervals f ^2pn (J), n= 0, 1, 2,…, is convergent. Translated from Neliniini Kolyvannya, Vol. 12, No. 1, pp. 130–133, January–March, 2009.     

Convergence of biorthogonal series of biharmonic eigenfunctions by the method of titchmarsh

Canonical edge problems for the biharmonic equation can be solved by separating variables. The eigenvalues and eigenvectors arising in this separation are derived from a reduced system of ordinary differential equations along lines suggested in the excellent work of R. C. Smith (1952). We study the reduced system which is governed by a vector ordinary differential equation. A solution of the biharmonic problem, governed by a partial differential equation, can be found only if the prescribed data is restricted to a subspace of the space spanned by the eigenfunctions of the reduced problem. The theory leads to problems in generalized harmonic analysis which seek conditions under which arbitrary vector fields f(y) with values in ² can be represented in terms of eigenvectors of the reduced problem. This paper adds new theorems and conjectures to the theory. We extend Smith's generalization to fourth-order problems of the methods introduced by Titchmarsh (1946) to study eigenfunction expansions associated with second-order problems. We use this method to prove that, if f(y)=[(f ₁(y), f ₂y)], -1y1, f(y) C¹[-1, 1], f L₂[-1, 1], then the series expressing f(y) converges uniformly to f(y) in the open interval (-1, 1), uniformly in [-1, 1] if f ₁(±1)=0 and, in any case, to [0, f ₂(±1)-f ₁(±1)] at y=±1. This is unlike Fourier series, which converge to the mean value of the periodic extension of a function. The series exhibits a Gibbs phenomenon near the end points of discontinuity when f ₁(±1) 0.The Gibbs undershoot and overshoot for the step function vector [1, 0] and ramp function vector [y, 0] are computed numerically. The undershoot and overshoot are much larger than in the case of Fourier series and, unlike Fourier series, the Gibbs oscillations do not appear to be entirely suppressed by Féjer's method of summing Cesaro sums. We show that, when f(y) has interior points of discontinuity, the series for f(y) diverges and we present numerical results which indicate that, in this divergent case, the Cesaro sums converge to f(y) apparently with Gibbs oscillations near the point of discontinuity.     

On Asymptotics of Solutions of Nonlinear Differential Equations of the Second Order

We study the problem of asymptotics of unbounded solutions of differential equations of the form y″ = α₀ p(t)ϕ(y), where α₀ ∈ {−1, 1}, p: [a, ω[→]0, +∞[, −∞ < a < ω ≤ +∞, is a continuous function, and ϕ: [y ₀, +∞[→]0, +∞[ is a twice continuously differentiable function close to a power function in a certain sense.__________Translated from Neliniini Kolyvannya, Vol. 8, No. 1, pp. 18–28, January–March, 2005.     

The effect of cold-work on the electrical resistivity of alloys and the law of recovery

Summary The change in resistivity due to cold-work has been determined for a number of binary alloy series having copper, silver or gold as basic metal. The effects observed are very different in the different alloy systems. A change as large as 42% of the total resistivity is found in one case. Alloys from the systems gold-chromium and gold-iron show a decrease of resistivity when cold-worked. In addition to the binary series, some alloys containing three or four components have also been investigated, and on the basis of the results obtained the question of the influence of the different solutes upon the change of resistivity is discussed. Results are given regarding the recovery of the resistivity changes as a function of time for different annealing temperatures. The resistivity change Δϱ as a function of temperatureT and time τ is found to obey the law Δϱ=cτ ⁿ exp (−nE/RT), wheren is a number of the order 0.1–0.4 andE is the activation energy of the process;R is the gas constant, andc a quantity of proportionality. Alloys belonging to the following binary systems have been investigated: Cu-Al, Cu-Si, Ag-Al, Ag-Mn, Ag-Sn, Au-Al, Au-Cr, Au-Mn, Au-Fe and Au-Sn, and the following multi-component systems: Au-Mn-Cr, Au-Mn-Cr-Fe and Au-Al-Cr.     

Improvement of cold-wire response for measurement of temperature dissipation

This work aimed at improving fine-scale measurements using cold-wire anemometry. The dissipation ɛ _θ of the temperature variance was measured on the axis of a heated turbulent round jet. The measurements were performed with a constant current anemometer (CCA) operating fine Pt–10%Rh wires at very low overheat. The CCA developed for this purpose allowed the use of the current injection method in order to estimate the time constant of the wire. In the first part of the paper, it is shown that the time constants obtained for two wire diameters −d=1.2 and d=0.58 μm – compare well with those measured at the same time using two other methods (laser excitation and pulsed wire). Moreover, for these two wires, the estimated time constants were in good agreement with those obtained from a semi-empirical relation. In the second part of the paper, a compensation procedure – post-processing filtering – was developed in order to improved the frequency response of the cold-wire probes. The measurements carried out on the axis of the jet (Re _D =16 500, Re _λ  ≃ 167) showed that the frequency response of the 1.2 μm wire was significantly improved. In fact, the spectral characteristics of the compensated signal obtained with the 1.2 μm wire compared fairly well with those from the 0.58 μm wire. Moreover, the results indicated that the compensation procedure must be applied when the cut-off frequency of the cold-wire f _c is lower than two times the Kolmogorov frequency f _K. In the case where f _c ≃ 0.6f _K, the compensation procedure can reduce the error in the estimate of ɛ _θ by more than 20%. When f _c ≃ 2f _K, the effect of the compensation is reduced to about 5%. Received: 3 November 2000/Accepted: 23 March 2001     

Optimization of the deflagration to detonation transition: reduction of length and time of transition

The aim of this experimental investigation is the study of Deflagration to Detonation Transition (DDT) in tubes in order to (i) reduce both run-up distance and time of transition (L _DDT and t _DDT) in connection with Pulsed Detonation Engine applications and to (ii) attempt to scale L _DDT with λ_CJ (the detonation cellular structure width). In DDT, the production of turbulence during the long flame run-up can lead to L _DDT values of several meters. To shorten L _DDT, an experimental set-up is designed to quickly induce highly turbulent initial flow. It consists of a double chamber terminated with a perforated plate of high Blockage Ratio (BR) positioned at the beginning of a 26 mm inner diameter tube containing a “Shchelkin spiral” of BR ≈ 0.5. The study involves stoichiometric reactive mixtures of H₂, CH₄, C₃H₈, and C₂H₄ with oxygen and diluted with N₂ in order to obtain the same cell width λ_CJ≈10 mm at standard conditions. The results show that a shock-flame system propagating with nearly the isobaric speed of sound of combustion products, called the choking regime, is rapidly obtained. This experimental set-up allows a L _DDT below 40 cm for the mixtures used and a ratio L _DDT/λ_CJ ranging from 23 to 37. The transition distance seems to depend on the reduced activation energy (E _a/RT _c) and on the normalized heat of reaction (Q/a ₀ ²). The higher these quantities are, the shorter the ratio L _DDT/λ_CJ is. PACS 47.40.Rs · 47.60.+i · 47.70.Pq · 47.80.CbThis paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003.     

Study of vibrational deactivation of molecules of carbon dioxide gas during cooling of stream in a supersonic nozzle

The vibrational temperature of the antisymmetrical type of vibrations (v ₃) of the CO₂ molecule at the exit of a supersonic nozzle is measured in the present work using the method of recording the infrared emission. Freezing in of thev ₃-type vibrations was observed during the flow of undiluted carbon dioxide in a nozzle. In this case the vibrational temperature T₃ considerably exceeded the translational temperature. On the basis of a comparison of the experimental results with calculation it can be concluded that vibrational deactivation of CO₂ molecules occurs three to five times faster than the excitation of the vibrations during heating in a shock wave. All the experiments were conducted under the following conditions: maximum expansion of gas in nozzle A/A* = 115, temperature range 1900–2400 °K, pressure range 1–17.5 atm.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 32–40, November–December, 1973.The authors are grateful to U. G. Pirumov and É. A. Ashratov for the calculation of the nozzle profile and the distribution of streamlines as well as for a discussion of the results.     

Some aspects of Euler-Newton equations of motion

Summary Euler-Newton's equations for a system of connected rigid bodies, written in a special state space form, provide a systematic method of arriving at the differential equations of the system. This method is amenable to programming and symbolic algebraic manipulation. The elimination of some or all forces of constraint is by projection, implementing the principle of virtual work, and is done by inner products. The computation of these forces requires symbolic inversion of a matrix for which an iterative scheme is proposed here. A method for construction of Lyapunov functions for stability of such systems in the vicinity of an arbitrary operating point is proposed. This construction may be achieved by symbolic manipulations and supplements applications of the Euler-Newton method.

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Einige Aspekte der Euler-Newtonschen Bewegungsgleichungen

Übersicht Euler-Newtonsche Gleichungen, dargestellt in einem besonderen Zustandsraum, liefern eine systematische Methode zur Herleitung der Differentialgleichungen eines Systems starr verbundener Körper. Diese Methode eignet sich für symbolisch algebraische Verfahren und zur Programmierung. Durch Projektion, unter Anwendung des Prinzips der virtuellen Arbeit und Berechnung der inneren Produkte, können einige oder alle Zwangskräfte eliminiert werden. Die Berechnung dieser Kräfte erfordert symbolische Matrixinversion, für die hier ein iteratives Verfahren vorgeschlagen wird. Ferner wird eine Methode vorgestellt, die zur Herleitung der Lyapunovschen Stabilitätsfunktion in der Umgebung eines beliebigen Arbeitspunktes dient. Die Lyapunovfunktion kann durch symbolische Verfahren und durch ergänzende Anwendungen der Euler-Newton Methode ermittelt werden.

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This work was supported in part by NSF under Grant ECS 782 4440 and in part by a fellowship grant from the Department of Transportation/NHTSA     

Experimental study of sedimentation characteristics of spheroidal particles

The drag of non-spherical particles is a basic, important parameter for multi-phase flow. As the first step in research in this area, the terminal velocities, Ut, of hemispherical and spherical segment particles with maximal diameters of 6-21 mm were measured in static fluids by using a high-speed video camera. The drag coefficient, CD, measured for Reynolds number, Re of 10^1-10^5, has been obtained and compared with those for a sphere. The Re based on the terminal velocity has a logarithmic linear relationship with Ar number for both the facet facing upwards or downwards for the two experimental spheroidal particles, and their Co values are greater than those of spheres. A shape function that depends on the initial orientation of the particle facet is presented to correct for the shape effects.